\chapter{The Rules of Time Chess} \label{rules}

For the purposes of this document, it is assumed that the reader is
generally familiar with the rules of standard Chess. Because Time
Chess is a `chess variant', it shares a substantial part of its
setup and rules with Chess.

\label{rules-of-time-chess}

\section{Board and Pieces}

Time Chess pieces are closely related to Chess pieces, and share
their names, symbols, appearances, and much of their behaviour. If
an aspect of a piece is not specified in this document, it may be
assumed that it shares that aspect with its equivalent in Chess.

Time Chess is conceptually played on a standard Chess board, and
could be played using one or more physical Chess boards, however
this would be impractical. \TC is only practically played on a
computer, which will generally model the game as a three
dimensional object which can be thought of as a stack of Chess
boards. Each layer of the stack archaeologically represents a turn
of the game, and the stack becomes taller (or deeper) as the game
progresses.

\section{Objective}

The objective of Time Chess is broadly the same as that of Chess -
To place the opponent's King `under attack', such that your
opponent has no legal moves.

\section{Movement}

\label{rules-movement} \label{movement-rules}

\TC piece movements can be thought of as Chess movements
generalised and extruded into a higher dimension. As well as moving
around the board as normal, pieces can move both forward and
backward in time. Their time travelling movement options closely
mirror their normal movement options.

\begin{itemize}
\item
  A Rook in Chess may pick a direction, $x+$, $x-$, $y+$ or $y-$ and
  move any number of places in that direction. So a Time Rook may
  pick a direction, $x+$, $x-$, $y+$, $y-$, $t+$ or $t-$, and move up
  to 7 of places in that direction. Positive movement in the $t$
  dimension is movement forwards in time, negative movement in the
  $t$ dimension is movement backwards in time.

\item
  A Bishop in Chess picks two orthogonal directions and moves an
  equal number of places in each of those directions, effectively
  moving diagonally. The same is true of a Time Bishop, but it also
  has the choice of $t+$ and $t-$ as directions. See Figure
  \ref{fig-bishopsmove}.

\end{itemize}
\newcommand{\xatk}{\raisebox{.5mm}{$\times$}}
\newcommand{\xmov}{\raisebox{.5mm}{$+$}}
\newcommand{\xmovs}{\raisebox{.5mm}{$\circ$}}
\newcommand{\xmovb}{\raisebox{.5mm}{$\bigcirc$}}

\newcommand{\circone}{\raisebox{.3mm}{$\bigcirc$}\nolinebreak\hspace{-2.8mm}$1$\nolinebreak\hspace{1mm}}
\newcommand{\circtwo}{\raisebox{.3mm}{$\bigcirc$}\hspace{-2.8mm}$2$\hspace{1mm}}

\input{bishopsmove.tex}

\begin{itemize}
\item
  A Knight in Chess picks two orthogonal directions, and moves two
  spaces in one dimension and one space in the other. Again, this is
  extruded into the higher dimension of time to provide the Time
  Knight movement shown in Figure \ref{fig-knightsmove}
  \input{knightsmove.tex}

\item
  A Queen in Chess picks either one direction or two orthogonal
  directions, and moves any number of places in those. This makes a
  Queen's possible move set effectively the union of the move sets of
  a Bishop and a Rook. The same is true of a Time Queen, as seen in
  Figure \ref{fig-queensmove}. \input{queensmove.tex}

\item
  A King in Chess can move one space in either one direction or in
  two orthogonal directions. The Time King's movement is the same
  with possibility of forwards and backwards in time as directions.
  \input{kingsmove.tex}

\item
  Time Pawn movement is show in figure \ref{fig-pawnsmove}. The Time
  Pawn can move to positions marked with \circone{} if they are
  unoccupied, and to positions marked with \circtwo{} if the pawn has
  not moved before, and the target position and the \circone{}
  position between the pawn and the target position are both
  unoccupied. It can capture opposing pieces in positions marked with
  an $\times$. \input{pawnsmove.tex}

\end{itemize}
\subsection{Blocking}

\label{blocking}

For all pieces other than the Knight, movement cannot be made
through an occupied space. This applies in time as well - for a
piece to move to a position, all the spaces in between must be
empty. Thus the location of pieces in past turns decides which
moves into the past are possible, and the locations of piece in the
future determines what moves into the future are possible.

\input{pastblocking.tex}

\section{Forward Time Travel}

When a player declares that they are moving a piece forward in
time, that piece is removed from the board. When the turn that the
piece was moved to comes around, at the end of that turn the piece
is placed at its destination.

\subsection{Appearance Order}

If two pieces are due to arrive from forward time travel in the
same turn, the one which departed first arrives first. This is
generally only significant if both pieces are arriving at the same
square at the same time.

\subsection{The `Lost in Time' Rule}

\label{lost-in-time-rule}

The legality of a forwards time travelling move is not necessarily
known at the time the move is made. This is because the move may
require certain spaces to be empty, but at the time the move is
made, the state of the spaces is yet to be determined. Thus it is
possible to render a forward time travelling move illegal after it
has been made. If this happens, the `in transit' time travelling
piece is said to become `Lost in Time'. A piece that is Lost in
Time is never returned to the board, and is \emph{hors de combat}.

Note that this makes something similar to an En Passant rule for
Pawn time travel, since a Pawn moving two spaces into the future
may become Lost in Time due to a piece moving into the space one
turn ahead of it.

If a king becomes Lost in Time, the owner of the king loses the
game.

\section{Backward Time Travel}

\label{rules-backward-time-travel} \label{backward-time-travel}

When a piece moves backwards in time, it is removed from its
present position, and placed at its destination position.

\subsection{Taking Pieces Back in Time}

\label{taking-pieces-back-in-time}

If a piece is captured in the past, all occurrences of the piece
from the time it is captured to the present are removed from the
game. Any consequences caused by the taken piece in the time
between its capture and the present (pieces it has taken, moves it
has made possible etc.) remain \textbf{unchanged}.

\subsection{Braindead Pieces and Steamrollering}

\label{braindead-pieces}

Since the players may only command pieces which are in the present,
when a piece moves into the past it cannot be given commands, and
thus will not move. Such a piece is said to be `braindead' in the
time between its arrival in the past, and the present. It is
propagated `upwards' towards the present in a straight line.

\label{steamrollering} While a piece is braindead, any piece of
either colour which moves into a space occupied by it, destroys it.
Naturally if an opposing piece happened, in the past, to move into
a space occupied by a braindead piece, it would capture it, but the
same is true of a piece of the same colour as the braindead piece.
This is called `steamrollering'. The steamrollering piece could not
have been ordered to move into an occupied space, but the space was
not occupied when the order was given, so the move goes ahead and
the braindead piece is steamrollered.

\section{Check}

\label{check-rules} \label{check}

Because pieces can be captured in the past, a King is in check if
it can be attacked in the present \emph{or} the past. If any past
instance of the King is under attack, the King is considered in
check.

